METAMATEMATIKA

METAMATEMATIKA, nazariyai isbot, nazariyai isbotho, ilmest, ki nazariyahoi shaklii matematiki va tarzu usuli isboti matematikiro tadqiq mekunad. Teoremahoe, ki ba yagon nazariyai matematiki (mas., arifmetika, geometriyai Evklid, nazariyai guruhho) oidand, du navand. Ba navi yakum tsoremahoe mansuband, ki tanho bo metodhoi nazariyai predmeti isbot karda meshavand. Ba navi duyum teoremahoe mansuband, ki isbotashon az doirai nazariyai mazkur berun mebaroyad. Chunin teoremaho bo yorii nazariyai umumitar va nisbatan murakkab, yane ba istiloh metanazariya va mafhumhoe isbot megardand, ki dar shakli matematiki ifoda nameshavand. Mas., teoremai Pifagorro bo usulhoi geometriyai Evklid isbot kardan mumkin ast. Az ziddiyati botini kholi budani geometriyai Evklid az khilofnopazirii nazariyai adadhoi haqiqi barmeoyad. Az in sabab, nazariyai adadhoi haqiqiro nisbat ba geometriya metavon metanazariya nomid. Aqoidi shaklii formalizmi matematikiro bori avval D. Gilbert pesh guzosht. Bo yorii metodhoi nazariyai matematiki isbot namudani az ziddiyati botini kholis budani arifmetika az nakhustin masalahoi in aqoid hisob yoft. S 1931 mantiqshinos va matematiki avstriyagi K. Gyodel nishon dod, ki az ziddiyati botini kholi budani arifmetikaro bo yorii hej yak nazariyai matematiki isbot kardan mumkin nest. Teoremahoi Gyodel ba inkishofi minbadai metamatematika takoni zur dod. Chunonchi, P. Kozn isbot kard, ki kontinumfarziyaro (nig. Problemoy Kontinuum) ba vositai usulhoi muqarrarii nazariyai majmu isbot kardan mumkin nest (1963). In az komyobihoi namoyoni metamatikai hozirazamon meboshad.

Ad.: Novikov P. S., Elementi matematicheskoy logiki, M., 1973; Klini S. K., Matematicheskaya logika, per. sangl., M., 1973.

A. Qurbonov.